{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating Moving Objects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the first few sections are not run in the Jupyter notebook.  You can rund `asteroids.py` from the command line and view that file directly in a text editor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Digging deeper into Euler’s method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 0\n",
    "s = (0,0)\n",
    "v = (1,0)\n",
    "a = (0,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 2\n",
    "steps = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vectors import add, scale\n",
    "positions = [s]\n",
    "for _ in range(0,5):\n",
    "    t += 2\n",
    "    s = add(s, scale(dt,v)) \n",
    "    v = add(v, scale(dt,a)) \n",
    "    positions.append(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from draw2d import *\n",
    "draw2d(Points2D(*positions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x396 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def pairs(lst):\n",
    "    return list(zip(lst[:-1],lst[1:]))\n",
    "\n",
    "def eulers_method(s0,v0,a,total_time,step_count):\n",
    "    positions = [s0]\n",
    "    s = s0\n",
    "    v = v0\n",
    "    dt = total_time/step_count\n",
    "    for _ in range(0,step_count):\n",
    "        s = add(s,scale(dt,v))\n",
    "        v = add(v,scale(dt,a))\n",
    "        positions.append(s)\n",
    "    return positions\n",
    "\n",
    "approx5 = eulers_method((0,0),(1,0),(0,0.2),10,5)\n",
    "approx10 = eulers_method((0,0),(1,0),(0,0.2),10,10)\n",
    "approx100 = eulers_method((0,0),(1,0),(0,0.2),10,100)\n",
    "approx1000 = eulers_method((0,0),(1,0),(0,0.2),10,1000)\n",
    "\n",
    "from draw2d import *\n",
    "draw2d(\n",
    "    Points2D(*approx5, color='C0'),\n",
    "    *[Segment2D(t,h,color='C0') for (h,t) in pairs(approx5)],\n",
    "    Points2D(*approx10, color='C1'),\n",
    "    *[Segment2D(t,h,color='C1') for (h,t) in pairs(approx10)]\n",
    "    )\n",
    "\n",
    "from draw2d import *\n",
    "draw2d(\n",
    "    Points2D(*approx5, color='C0'),\n",
    "    *[Segment2D(t,h,color='C0') for (h,t) in pairs(approx5)],\n",
    "    Points2D(*approx10, color='C1'),\n",
    "    *[Segment2D(t,h,color='C1') for (h,t) in pairs(approx10)],\n",
    "    *[Segment2D(t,h,color='C2') for (h,t) in pairs(approx100)],\n",
    "    save_as='../3eulers.svg'\n",
    "    )\n",
    "\n",
    "draw2d(\n",
    "    Points2D(*approx5, color='C0'),\n",
    "    *[Segment2D(t,h,color='C0') for (h,t) in pairs(approx5)],\n",
    "    Points2D(*approx10, color='C1'),\n",
    "    *[Segment2D(t,h,color='C1') for (h,t) in pairs(approx10)],\n",
    "    *[Segment2D(t,h,color='C2') for (h,t) in pairs(approx100)],\n",
    "    *[Segment2D(t,h,color='C3') for (h,t) in pairs(approx1000)],\n",
    "    )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
